Minimum of the modulus of an entire function on the sequence of Polya peaks

A. E. Eremenko; M. L. Sodin; D. F. Shia (Shea)

doi:10.1007/BF01097569

Minimum of the modulus of an entire function on the sequence of Polya peaks

A. E. Eremenko, M. L. Sodin, D. F. Shia (Shea)

School of Mathematical Sciences

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Abstract

Let f be an entire function of genus zero, let (r_k) be a sequence of Pólya peaks for N(r, f) of order λ<1. Then there exists a sequence r_k^′~r_k such that[Figure not available: see fulltext.] If for (r_k) one takes a sequence of Pólya peaks for ln M(r, f) or for T(r, f), 1/2<λ<1, then the result ceases to be true.

Original language	English
Pages (from-to)	386-398
Number of pages	13
Journal	Journal of Soviet Mathematics
Volume	48
Issue number	4
DOIs	https://doi.org/10.1007/BF01097569
State	Published - Feb 1990

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abstract = "Let f be an entire function of genus zero, let (rk) be a sequence of P{\'o}lya peaks for N(r, f) of order λ<1. Then there exists a sequence rk′~rk such that[Figure not available: see fulltext.] If for (rk) one takes a sequence of P{\'o}lya peaks for ln M(r, f) or for T(r, f), 1/2<λ<1, then the result ceases to be true.",

author = "Eremenko, {A. E.} and Sodin, {M. L.} and {Shia (Shea)}, {D. F.}",

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N2 - Let f be an entire function of genus zero, let (rk) be a sequence of Pólya peaks for N(r, f) of order λ<1. Then there exists a sequence rk′~rk such that[Figure not available: see fulltext.] If for (rk) one takes a sequence of Pólya peaks for ln M(r, f) or for T(r, f), 1/2<λ<1, then the result ceases to be true.

AB - Let f be an entire function of genus zero, let (rk) be a sequence of Pólya peaks for N(r, f) of order λ<1. Then there exists a sequence rk′~rk such that[Figure not available: see fulltext.] If for (rk) one takes a sequence of Pólya peaks for ln M(r, f) or for T(r, f), 1/2<λ<1, then the result ceases to be true.

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Minimum of the modulus of an entire function on the sequence of Polya peaks

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